\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\@writefile{toc}{\contentsline {section}{\numberline {1}Material Models for Structural Analysis}{6}{section.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Elastic materials}{6}{subsection.1.1}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}Isotropic linear elastic material - IsoLE}{6}{subsubsection.1.1.1}}
\newlabel{IsoLE}{{1.1.1}{6}{Isotropic linear elastic material - IsoLE}{subsubsection.1.1.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Linear Isotropic Material - summary.}}{6}{table.1}}
\newlabel{IsoLE_table}{{1}{6}{Linear Isotropic Material - summary}{table.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}Orthotropic linear elastic material - OrthoLE}{6}{subsubsection.1.1.2}}
\newlabel{OrthoLE}{{1.1.2}{6}{Orthotropic linear elastic material - OrthoLE}{subsubsection.1.1.2}{}}
\citation{SimoHughes}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}General anisotropic linear elastic material - AnisoLE}{7}{subsubsection.1.1.3}}
\newlabel{AnisoLE}{{1.1.3}{7}{General anisotropic linear elastic material - AnisoLE}{subsubsection.1.1.3}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.4}Hyperelastic material - HyperMat}{7}{subsubsection.1.1.4}}
\newlabel{freeEnergy}{{9}{7}{Hyperelastic material - HyperMat}{equation.1.9}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Orthotropic, linear elastic material -- summary.}}{8}{table.2}}
\newlabel{OrthoLE_table}{{2}{8}{Orthotropic, linear elastic material -- summary}{table.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Anisotropic, linear elastic material -- summary.}}{8}{table.3}}
\newlabel{AnisoLE_table}{{3}{8}{Anisotropic, linear elastic material -- summary}{table.3}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.5}Hyperelastic material - Compressible Mooney-Rivlin}{8}{subsubsection.1.1.5}}
\newlabel{freeEnergyMR}{{11}{8}{Hyperelastic material - Compressible Mooney-Rivlin}{equation.1.11}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Hyperelastic material - summary.}}{9}{table.4}}
\newlabel{hyperElMat_table}{{4}{9}{Hyperelastic material - summary}{table.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Winkler-Pasternak model}{9}{subsection.1.2}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Compressible Mooney-Rivlin - summary.}}{10}{table.5}}
\newlabel{MooneyRivlin_table}{{5}{10}{Compressible Mooney-Rivlin - summary}{table.5}{}}
\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Winkler Pasternak material - summary.}}{10}{table.6}}
\newlabel{WinklerPasternak_table}{{6}{10}{Winkler Pasternak material - summary}{table.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Large-strain master material}{10}{subsection.1.3}}
\newlabel{generalizedStrainMeasures}{{18}{10}{Large-strain master material}{equation.1.18}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Plasticity-based material models}{10}{subsection.1.4}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.1}Drucker-Prager model - DruckerPrager}{10}{subsubsection.1.4.1}}
\newlabel{DPmodel}{{1.4.1}{10}{Drucker-Prager model - DruckerPrager}{subsubsection.1.4.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Large-strain master material material - summary.}}{11}{table.7}}
\newlabel{LSmasterMat_table}{{7}{11}{Large-strain master material material - summary}{table.7}{}}
\newlabel{eq:equivalentStress}{{20}{11}{Drucker-Prager model - DruckerPrager}{equation.1.20}{}}
\newlabel{eq:elasticLaw}{{24}{11}{Drucker-Prager model - DruckerPrager}{equation.1.24}{}}
\newlabel{eq:softeningLaw}{{25}{11}{Drucker-Prager model - DruckerPrager}{equation.1.24}{}}
\newlabel{eq:flowRule}{{26}{11}{Drucker-Prager model - DruckerPrager}{equation.1.24}{}}
\newlabel{eq:hardening}{{27}{11}{Drucker-Prager model - DruckerPrager}{equation.1.24}{}}
\newlabel{eq:loading}{{28}{11}{Drucker-Prager model - DruckerPrager}{equation.1.28}{}}
\newlabel{eq:kFactor}{{29}{12}{Drucker-Prager model - DruckerPrager}{equation.1.29}{}}
\newlabel{bilin-soft}{{30}{12}{Drucker-Prager model - DruckerPrager}{equation.1.30}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.2}Drucker-Prager model with tension cut-off and isotropic damage - DruckerPragerCut}{12}{subsubsection.1.4.2}}
\newlabel{DPCutmodel}{{1.4.2}{12}{Drucker-Prager model with tension cut-off and isotropic damage - DruckerPragerCut}{subsubsection.1.4.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces DP material - summary.}}{13}{table.8}}
\newlabel{DP_table}{{8}{13}{DP material - summary}{table.8}{}}
\newlabel{damagelawDP}{{37}{13}{Drucker-Prager model with tension cut-off and isotropic damage - DruckerPragerCut}{equation.1.37}{}}
\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Drucker Prager material with tension cut-off - summary.}}{14}{table.9}}
\newlabel{DP_table_cut}{{9}{14}{Drucker Prager material with tension cut-off - summary}{table.9}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.3}Mises plasticity model with isotropic damage - MisesMat}{15}{subsubsection.1.4.3}}
\newlabel{sec:misplast}{{1.4.3}{15}{Mises plasticity model with isotropic damage - MisesMat}{subsubsection.1.4.3}{}}
\@writefile{toc}{\contentsline {paragraph}{Small-strain formulation:}{15}{section*.3}}
\newlabel{VMadditiveDecomposition}{{38}{15}{Small-strain formulation:}{equation.1.38}{}}
\newlabel{VMconstitutiveEquation}{{39}{15}{Small-strain formulation:}{equation.1.39}{}}
\newlabel{VMvonMisesCondition}{{40}{15}{Small-strain formulation:}{equation.1.40}{}}
\newlabel{VMcumPlasStrain}{{41}{15}{Small-strain formulation:}{equation.1.41}{}}
\newlabel{VMlinearHardeningLaw}{{42}{15}{Small-strain formulation:}{equation.1.42}{}}
\newlabel{VMkuhnTucker}{{44}{15}{Small-strain formulation:}{equation.1.44}{}}
\newlabel{damagelawmp}{{45}{15}{Small-strain formulation:}{equation.1.45}{}}
\citation{SimoHughes}
\@writefile{toc}{\contentsline {paragraph}{Large-strain formulation}{16}{section*.4}}
\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Mises plasticity -- summary.}}{16}{table.10}}
\newlabel{misesMat_table}{{10}{16}{Mises plasticity -- summary}{table.10}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.4}Mises plasticity model with isotropic damage, nonlocal - MisesMatNl, MisesMatGrad}{16}{subsubsection.1.4.4}}
\newlabel{overKappa1}{{47}{16}{Mises plasticity model with isotropic damage, nonlocal - MisesMatNl, MisesMatGrad}{equation.1.47}{}}
\@writefile{toc}{\contentsline {paragraph}{Integral nonlocal formulation}{16}{section*.5}}
\newlabel{nonLocalPlStrain1}{{48}{16}{Integral nonlocal formulation}{equation.1.48}{}}
\newlabel{alpha0}{{50}{17}{Integral nonlocal formulation}{equation.1.50}{}}
\@writefile{toc}{\contentsline {paragraph}{Implicit gradient formulation}{17}{section*.6}}
\newlabel{implicitGradient}{{51}{17}{Implicit gradient formulation}{equation.1.51}{}}
\newlabel{neumannBC}{{52}{17}{Implicit gradient formulation}{equation.1.52}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.5}Rankine plasticity model with isotropic damage and its nonlocal formulations - RankMat, RankMatNl, RankMatGrad}{17}{subsubsection.1.4.5}}
\newlabel{sec:rankplast}{{1.4.5}{17}{Rankine plasticity model with isotropic damage and its nonlocal formulations - RankMat, RankMatNl, RankMatGrad}{subsubsection.1.4.5}{}}
\newlabel{RankineCondition}{{53}{17}{Rankine plasticity model with isotropic damage and its nonlocal formulations - RankMat, RankMatNl, RankMatGrad}{equation.1.53}{}}
\newlabel{VMexpHardeningLaw}{{54}{17}{Rankine plasticity model with isotropic damage and its nonlocal formulations - RankMat, RankMatNl, RankMatGrad}{equation.1.54}{}}
\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Nonlocal integral Mises plasticity -- summary.}}{18}{table.11}}
\newlabel{misesMatNl_table}{{11}{18}{Nonlocal integral Mises plasticity -- summary}{table.11}{}}
\citation{Rots}
\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Gradient-enhanced Mises plasticity -- summary.}}{19}{table.12}}
\newlabel{misesMatGrad_table}{{12}{19}{Gradient-enhanced Mises plasticity -- summary}{table.12}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.6}Perfectly plastic material with Mises yield condition - Steel1}{19}{subsubsection.1.4.6}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.7}Composite plasticity model for masonry - Masonry02}{19}{subsubsection.1.4.7}}
\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Rankine plasticity -- summary.}}{20}{table.13}}
\newlabel{rankineMat_table}{{13}{20}{Rankine plasticity -- summary}{table.13}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Composite yield surface model for masonry}}{20}{figure.1}}
\newlabel{compyieldsurffig}{{1}{20}{Composite yield surface model for masonry}{figure.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {14}{\ignorespaces Nonlocal integral Rankine plasticity -- summary.}}{21}{table.14}}
\newlabel{rankineMatNl_table}{{14}{21}{Nonlocal integral Rankine plasticity -- summary}{table.14}{}}
\@writefile{lot}{\contentsline {table}{\numberline {15}{\ignorespaces Gradient-enhanced Rankine plasticity -- summary.}}{22}{table.15}}
\newlabel{rankineMatGrad_table}{{15}{22}{Gradient-enhanced Rankine plasticity -- summary}{table.15}{}}
\@writefile{lot}{\contentsline {table}{\numberline {16}{\ignorespaces Perfectly plastic material with Mises condition -- summary.}}{22}{table.16}}
\newlabel{Steel1_table}{{16}{22}{Perfectly plastic material with Mises condition -- summary}{table.16}{}}
\@writefile{toc}{\contentsline {paragraph}{Tension mode}{22}{section*.7}}
\newlabel{ft}{{58}{22}{Tension mode}{equation.1.58}{}}
\citation{Rots}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Modeling strategy for masonry}}{23}{figure.2}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Tensile behavior of proposed model ($f_t=0.2$ MPa, $G_f^I=0.018$ N/mm)}}{23}{figure.3}}
\newlabel{tensfig}{{3}{23}{Tensile behavior of proposed model ($f_t=0.2$ MPa, $G_f^I=0.018$ N/mm)}{figure.3}{}}
\@writefile{toc}{\contentsline {paragraph}{Shear mode}{23}{section*.8}}
\newlabel{c}{{60}{23}{Shear mode}{equation.1.60}{}}
\citation{Rots}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Shear behavior of proposed model for different confinement levels in MPa ($c_0=0.8\ \rm  {MPa},\ \qopname  \relax o{tan}\phi _0=1.0,\ \qopname  \relax o{tan}\phi _r=0.75,{\rm  and}\ G_f^{II}=0.05\ {N/mm}$)}}{24}{figure.4}}
\@writefile{toc}{\contentsline {paragraph}{Coupling of tension/shear modes}{24}{section*.9}}
\@writefile{toc}{\contentsline {paragraph}{Cap mode}{24}{section*.10}}
\newlabel{hs3}{{66}{25}{Cap mode}{equation.1.66}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Hardening/softening law for cap mode}}{25}{figure.5}}
\newlabel{hs3fig}{{5}{25}{Hardening/softening law for cap mode}{figure.5}{}}
\@writefile{lot}{\contentsline {table}{\numberline {17}{\ignorespaces Composite model for masonry - summary.}}{26}{table.17}}
\newlabel{compomasonry1_table}{{17}{26}{Composite model for masonry - summary}{table.17}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.8}Nonlinear elasto-plastic material model for concrete plates and shells - Concrete2}{26}{subsubsection.1.4.8}}
\newlabel{Rer}{{1.4.8}{26}{Nonlinear elasto-plastic material model for concrete plates and shells - Concrete2}{subsubsection.1.4.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5}Material models for tensile failure}{26}{subsection.1.5}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.1}Nonlinear elasto-plastic material model for concrete plates and shells - Concrete2}{26}{subsubsection.1.5.1}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}Smeared rotating crack model - Concrete3}{26}{subsubsection.1.5.2}}
\newlabel{rcm}{{1.5.2}{26}{Smeared rotating crack model - Concrete3}{subsubsection.1.5.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {18}{\ignorespaces Nonlinear elasto-plastic material model for concrete - summary.}}{27}{table.18}}
\newlabel{Rer_table}{{18}{27}{Nonlinear elasto-plastic material model for concrete - summary}{table.18}{}}
\@writefile{lot}{\contentsline {table}{\numberline {19}{\ignorespaces Rotating crack model for concrete - summary.}}{28}{table.19}}
\newlabel{rcm_table}{{19}{28}{Rotating crack model for concrete - summary}{table.19}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}Smeared rotating crack model with transition to scalar damage - linear softening - RCSD}{28}{subsubsection.1.5.3}}
\newlabel{rcsd}{{1.5.3}{28}{Smeared rotating crack model with transition to scalar damage - linear softening - RCSD}{subsubsection.1.5.3}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.4}Smeared rotating crack model with transition to scalar damage - exponential softening - RCSDE}{28}{subsubsection.1.5.4}}
\newlabel{rcsde}{{1.5.4}{28}{Smeared rotating crack model with transition to scalar damage - exponential softening - RCSDE}{subsubsection.1.5.4}{}}
\@writefile{lot}{\contentsline {table}{\numberline {20}{\ignorespaces RC-SD model for concrete - summary.}}{29}{table.20}}
\newlabel{rcsd_table}{{20}{29}{RC-SD model for concrete - summary}{table.20}{}}
\@writefile{lot}{\contentsline {table}{\numberline {21}{\ignorespaces RC-SD model for concrete - summary.}}{29}{table.21}}
\newlabel{rcsde_table}{{21}{29}{RC-SD model for concrete - summary}{table.21}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.5}Nonlocal smeared rotating crack model with transition to scalar damage - RCSDNL}{29}{subsubsection.1.5.5}}
\newlabel{rcsdnl}{{1.5.5}{29}{Nonlocal smeared rotating crack model with transition to scalar damage - RCSDNL}{subsubsection.1.5.5}{}}
\@writefile{lot}{\contentsline {table}{\numberline {22}{\ignorespaces RC-SD-NL model for concrete - summary.}}{30}{table.22}}
\newlabel{rcsdnl_table}{{22}{30}{RC-SD-NL model for concrete - summary}{table.22}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.6}Isotropic damage model for tensile failure - Idm1}{30}{subsubsection.1.5.6}}
\newlabel{sec:idmtf}{{1.5.6}{30}{Isotropic damage model for tensile failure - Idm1}{subsubsection.1.5.6}{}}
\citation{Vree:95}
\citation{Hoek}
\newlabel{mazars}{{69}{31}{Isotropic damage model for tensile failure - Idm1}{equation.1.69}{}}
\newlabel{rankinesmooth}{{70}{31}{Isotropic damage model for tensile failure - Idm1}{equation.1.70}{}}
\newlabel{rankinestandard}{{71}{31}{Isotropic damage model for tensile failure - Idm1}{equation.1.70}{}}
\newlabel{energynorm}{{72}{31}{Isotropic damage model for tensile failure - Idm1}{equation.1.72}{}}
\newlabel{modifiedmises}{{73}{31}{Isotropic damage model for tensile failure - Idm1}{equation.1.73}{}}
\newlabel{griffith1}{{74}{31}{Isotropic damage model for tensile failure - Idm1}{equation.1.74}{}}
\newlabel{griffith2}{{75}{32}{Isotropic damage model for tensile failure - Idm1}{equation.1.75}{}}
\citation{GraJir10}
\newlabel{eq:damageEvol}{{76}{35}{Isotropic damage model for tensile failure - Idm1}{equation.1.76}{}}
\newlabel{eqparams1}{{77}{35}{Isotropic damage model for tensile failure - Idm1}{equation.1.77}{}}
\newlabel{eqparams2}{{78}{35}{Isotropic damage model for tensile failure - Idm1}{equation.1.77}{}}
\newlabel{eqparams3}{{79}{35}{Isotropic damage model for tensile failure - Idm1}{equation.1.77}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Implemented stress-strain diagrams for isotropic damage material. Fracturing strain $\varepsilon _f$ and crack opening at zero stress $w_f$ are interrelated through effective thickness $h$ of the crack band. Note that exponential softening approach based on an exponential cohesive law is not exactly equivalent to the approach based on an exponential softening branch of the stress-strain diagram; see the detailed discussion of the damage laws.}}{35}{figure.6}}
\newlabel{idm_softening}{{6}{35}{Implemented stress-strain diagrams for isotropic damage material. Fracturing strain $\varepsilon _f$ and crack opening at zero stress $w_f$ are interrelated through effective thickness $h$ of the crack band. Note that exponential softening approach based on an exponential cohesive law is not exactly equivalent to the approach based on an exponential softening branch of the stress-strain diagram; see the detailed discussion of the damage laws}{figure.6}{}}
\gdef \LT@i {\LT@entry 
    {2}{88.19464pt}\LT@entry 
    {1}{268.0748pt}}
\@writefile{lot}{\contentsline {table}{\numberline {23}{Isotropic damage model for tensile failure -- summary.}}{37}{table.23}}
\newlabel{id_table}{{23}{37}{Isotropic damage model for tensile failure -- summary}{table.23}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.7}Nonlocal isotropic damage model for tensile failure - Idmnl1}{37}{subsubsection.1.5.7}}
\newlabel{sec:nidm}{{1.5.7}{37}{Nonlocal isotropic damage model for tensile failure - Idmnl1}{subsubsection.1.5.7}{}}
\citation{Gra14}
\citation{Gra14}
\citation{Gra14}
\@writefile{lot}{\contentsline {table}{\numberline {24}{\ignorespaces Nonlocal isotropic damage model for tensile failure -- summary.}}{40}{table.24}}
\newlabel{idnl_table}{{24}{40}{Nonlocal isotropic damage model for tensile failure -- summary}{table.24}{}}
\@writefile{lot}{\contentsline {table}{\numberline {25}{\ignorespaces Nonlocal isotropic damage model for tensile failure -- continued.}}{41}{table.25}}
\newlabel{idnl_table_cont}{{25}{41}{Nonlocal isotropic damage model for tensile failure -- continued}{table.25}{}}
\citation{mdm}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.8}Anisotropic damage model - Mdm}{42}{subsubsection.1.5.8}}
\@writefile{toc}{\contentsline {paragraph}{Local formulation}{42}{section*.11}}
\@writefile{lot}{\contentsline {table}{\numberline {26}{\ignorespaces Basic equations of microplane-based anisotropic damage model}}{42}{table.26}}
\newlabel{tab2}{{26}{42}{Basic equations of microplane-based anisotropic damage model}{table.26}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Structure of microplane-based anisotropic damage model}}{42}{figure.7}}
\newlabel{ff4}{{7}{42}{Structure of microplane-based anisotropic damage model}{figure.7}{}}
\newlabel{damcom}{{80}{43}{Local formulation}{equation.1.80}{}}
\newlabel{ee27}{{81}{43}{Local formulation}{equation.1.81}{}}
\newlabel{ee24}{{82}{43}{Local formulation}{equation.1.82}{}}
\newlabel{expsoft2}{{85}{43}{Local formulation}{equation.1.85}{}}
\newlabel{ee37}{{86}{44}{Local formulation}{equation.1.86}{}}
\@writefile{toc}{\contentsline {paragraph}{Nonlocal formulation}{44}{section*.12}}
\newlabel{psinl1}{{87}{44}{Nonlocal formulation}{equation.1.87}{}}
\@writefile{toc}{\contentsline {paragraph}{Input Record}{44}{section*.13}}
\@writefile{lot}{\contentsline {table}{\numberline {27}{\ignorespaces MDM model - summary.}}{45}{table.27}}
\newlabel{mdm_table}{{27}{45}{MDM model - summary}{table.27}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.9}Isotropic damage model for interfaces}{46}{subsubsection.1.5.9}}
\newlabel{sec:idmfi}{{1.5.9}{46}{Isotropic damage model for interfaces}{subsubsection.1.5.9}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.10}Isotropic damage model for interfaces using tabulated data for damage}{46}{subsubsection.1.5.10}}
\newlabel{sec:idmfiTabulated}{{1.5.10}{46}{Isotropic damage model for interfaces using tabulated data for damage}{subsubsection.1.5.10}{}}
\@writefile{lot}{\contentsline {table}{\numberline {28}{\ignorespaces Isotropic damage model for interface elements -- summary.}}{47}{table.28}}
\newlabel{iid_table}{{28}{47}{Isotropic damage model for interface elements -- summary}{table.28}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6}Material models specific to concrete}{47}{subsection.1.6}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.1}Mazars damage model for concrete - MazarsModel}{47}{subsubsection.1.6.1}}
\@writefile{lot}{\contentsline {table}{\numberline {29}{\ignorespaces Isotropic damage model for interface elements using tabulated data for damage -- summary.}}{48}{table.29}}
\newlabel{iidTabulated_table}{{29}{48}{Isotropic damage model for interface elements using tabulated data for damage -- summary}{table.29}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.2}Nonlocal Mazars damage model for concrete - MazarsModelnl}{48}{subsubsection.1.6.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.3}CebFip78 model for concrete creep with aging - CebFip78}{48}{subsubsection.1.6.3}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.4}Double-power law model for concrete creep with aging - DoublePowerLaw}{48}{subsubsection.1.6.4}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.5}Eurocode 2 model for concrete creep and shrinkage - EC2CreepMat}{48}{subsubsection.1.6.5}}
\@writefile{lot}{\contentsline {table}{\numberline {30}{\ignorespaces Mazars damage model -- summary.}}{49}{table.30}}
\newlabel{maz_table}{{30}{49}{Mazars damage model -- summary}{table.30}{}}
\@writefile{lot}{\contentsline {table}{\numberline {31}{\ignorespaces Nonlocal Mazars damage model -- summary.}}{50}{table.31}}
\newlabel{maznl_table}{{31}{50}{Nonlocal Mazars damage model -- summary}{table.31}{}}
\@writefile{lot}{\contentsline {table}{\numberline {32}{\ignorespaces CebFip78 material model -- summary.}}{50}{table.32}}
\newlabel{cebfip_table}{{32}{50}{CebFip78 material model -- summary}{table.32}{}}
\@writefile{lot}{\contentsline {table}{\numberline {33}{\ignorespaces Double-power law model -- summary.}}{51}{table.33}}
\newlabel{doublepowerlaw_table}{{33}{51}{Double-power law model -- summary}{table.33}{}}
\citation{Bazant-89-I}
\citation{Bazant-97-I}
\citation{JirHav14a}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.6}B3 and MPS models for concrete creep with aging}{52}{subsubsection.1.6.6}}
\newlabel{eq:mps_viscosity}{{112}{53}{B3 and MPS models for concrete creep with aging}{equation.1.112}{}}
\newlabel{eq:mps_temperature}{{113}{54}{B3 and MPS models for concrete creep with aging}{equation.1.113}{}}
\newlabel{dtedt}{{114}{54}{B3 and MPS models for concrete creep with aging}{equation.1.114}{}}
\newlabel{eq:mps_reformulate}{{123}{55}{B3 and MPS models for concrete creep with aging}{equation.1.123}{}}
\newlabel{eq:mps_p}{{124}{55}{B3 and MPS models for concrete creep with aging}{equation.1.124}{}}
\newlabel{eq:mps_k3}{{125}{55}{B3 and MPS models for concrete creep with aging}{equation.1.125}{}}
\newlabel{eq:auto_shr_b4}{{126}{55}{B3 and MPS models for concrete creep with aging}{equation.1.126}{}}
\newlabel{eq:auto_shr_fib}{{127}{55}{B3 and MPS models for concrete creep with aging}{equation.1.127}{}}
\newlabel{eq:auto_ultimate_B4}{{128}{55}{B3 and MPS models for concrete creep with aging}{equation.1.128}{}}
\newlabel{eq:auto_ultimate_fib}{{129}{56}{B3 and MPS models for concrete creep with aging}{equation.1.129}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.7}MPS damage model}{59}{subsubsection.1.6.7}}
\newlabel{gf}{{138}{60}{MPS damage model}{equation.1.138}{}}
\newlabel{gf_time}{{139}{60}{MPS damage model}{equation.1.139}{}}
\newlabel{fcm}{{140}{60}{MPS damage model}{equation.1.140}{}}
\@writefile{lot}{\contentsline {table}{\numberline {34}{\ignorespaces EC2Creep material model -- summary.}}{62}{table.34}}
\newlabel{ec2creep_table}{{34}{62}{EC2Creep material model -- summary}{table.34}{}}
\@writefile{lot}{\contentsline {table}{\numberline {35}{\ignorespaces B3 creep and shrinkage model -- summary.}}{63}{table.35}}
\newlabel{b3_table}{{35}{63}{B3 creep and shrinkage model -- summary}{table.35}{}}
\@writefile{lot}{\contentsline {table}{\numberline {36}{\ignorespaces B3solid creep and shrinkage model -- summary.}}{65}{table.36}}
\newlabel{b3solid_table}{{36}{65}{B3solid creep and shrinkage model -- summary}{table.36}{}}
\@writefile{lot}{\contentsline {table}{\numberline {37}{\ignorespaces MPS theory---summary.}}{67}{table.37}}
\newlabel{mps_table}{{37}{67}{MPS theory---summary}{table.37}{}}
\@writefile{lot}{\contentsline {table}{\numberline {38}{\ignorespaces MPS damage--summary.}}{68}{table.38}}
\newlabel{mps_dam_table}{{38}{68}{MPS damage--summary}{table.38}{}}
\citation{GraJir}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.8}Microplane model M4 - Microplane\_M4}{69}{subsubsection.1.6.8}}
\@writefile{lot}{\contentsline {table}{\numberline {39}{\ignorespaces Microplane model M4 -- summary.}}{69}{table.39}}
\newlabel{m4_table}{{39}{69}{Microplane model M4 -- summary}{table.39}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.9}Damage-plastic model for concrete - ConcreteDPM}{69}{subsubsection.1.6.9}}
\newlabel{sec:cdpm}{{1.6.9}{69}{Damage-plastic model for concrete - ConcreteDPM}{subsubsection.1.6.9}{}}
\newlabel{lodeangle}{{142}{69}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.142}{}}
\newlabel{eq:yieldSurface}{{143}{70}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.143}{}}
\newlabel{bf103}{{144}{70}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.144}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Evolution of the yield surface during hardening: a) meridional section, b) deviatoric section for a constant volumetric effective stress of $\mathaccentV {bar}016{\sigma }_{\rm  V} = -\mathaccentV {bar}016{f}_c/3$}}{70}{figure.8}}
\newlabel{fig:surfaceMerDev}{{8}{70}{Evolution of the yield surface during hardening: a) meridional section, b) deviatoric section for a constant volumetric effective stress of $\bar {\sigma }_{\rm V} = -\fc /3$}{figure.8}{}}
\citation{GraJir}
\newlabel{eq:failureSurface}{{145}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.145}{}}
\newlabel{eq:flowRuleDPM}{{146}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.146}{}}
\newlabel{eq:plasticPotential}{{147}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.147}{}}
\newlabel{eq:mg}{{148}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.148}{}}
\newlabel{eq:hardeningLaw}{{149}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.149}{}}
\newlabel{eq:dotkappap}{{150}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.150}{}}
\newlabel{eq:hardeningMeasure}{{151}{71}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.151}{}}
\newlabel{eq:equivStrain}{{155}{72}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.155}{}}
\newlabel{eq:damageDuctility}{{156}{72}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.156}{}}
\newlabel{eq:xs}{{157}{72}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.157}{}}
\newlabel{eq:damageLaw}{{158}{72}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.158}{}}
\@writefile{lot}{\contentsline {table}{\numberline {40}{\ignorespaces Damage-plastic model for concrete -- summary.}}{73}{table.40}}
\newlabel{dpm_table}{{40}{73}{Damage-plastic model for concrete -- summary}{table.40}{}}
\citation{GraJir}
\newlabel{eq:damageLaw2}{{159}{74}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.159}{}}
\newlabel{eq:damageLaw4}{{161}{74}{Damage-plastic model for concrete - ConcreteDPM}{equation.1.161}{}}
\citation{GraXenNys13}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.10}CDPM2}{75}{subsubsection.1.6.10}}
\newlabel{eqcdpm2:yieldSurface}{{166}{76}{CDPM2}{equation.1.166}{}}
\newlabel{eq:rFunction}{{167}{76}{CDPM2}{equation.1.167}{}}
\newlabel{eq:frictionM}{{168}{76}{CDPM2}{equation.1.168}{}}
\newlabel{eq:generalFlow}{{169}{76}{CDPM2}{equation.1.169}{}}
\newlabel{eq:detailedFlow}{{170}{76}{CDPM2}{equation.1.170}{}}
\newlabel{eq:hardeningLawOne}{{171}{76}{CDPM2}{equation.1.171}{}}
\newlabel{eq:hardeningLawTwo}{{172}{76}{CDPM2}{equation.1.172}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.11}Fixed crack model for concrete - ConcreteFCM}{78}{subsubsection.1.6.11}}
\newlabel{concreteFCM}{{1.6.11}{78}{Fixed crack model for concrete - ConcreteFCM}{subsubsection.1.6.11}{}}
\gdef \LT@ii {\LT@entry 
    {2}{88.19464pt}\LT@entry 
    {1}{268.0748pt}}
\@writefile{lot}{\contentsline {table}{\numberline {42}{Fixed crack model for concrete -- summary.}}{80}{table.42}}
\newlabel{concrete_fcm_table}{{42}{80}{Fixed crack model for concrete -- summary}{table.42}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.12}Fixed crack model for fiber reinforced composites - FRCFCM}{80}{subsubsection.1.6.12}}
\gdef \LT@iii {\LT@entry 
    {2}{88.19464pt}\LT@entry 
    {1}{268.0748pt}}
\gdef \LT@iv {\LT@entry 
    {1}{88.19464pt}\LT@entry 
    {1}{268.0748pt}}
\@writefile{lot}{\contentsline {table}{\numberline {43}{Fixed crack model for fiber reinforced concrete -- summary.}}{84}{table.43}}
\newlabel{frcfcm_table}{{43}{84}{Fixed crack model for fiber reinforced concrete -- summary}{table.43}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.13}``Nonlocal'' model for SHCC}{84}{subsubsection.1.6.13}}
\@writefile{lot}{\contentsline {table}{\numberline {44}{Nonlocal fixed crack model for fiber reinforced concrete -- summary.}}{84}{table.44}}
\newlabel{frcfcmnl_table}{{44}{84}{Nonlocal fixed crack model for fiber reinforced concrete -- summary}{table.44}{}}
\citation{Bazant:98}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7}Orthotropic damage model with fixed crack orientations for composites - CompDamMat}{85}{subsection.1.7}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Implemented stress-strain evolution with damage for 1D case. Tension and compression are separated, but sharing the same damage parameter.}}{85}{figure.9}}
\newlabel{comp_softening}{{9}{85}{Implemented stress-strain evolution with damage for 1D case. Tension and compression are separated, but sharing the same damage parameter}{figure.9}{}}
\newlabel{comp_eq_H}{{200}{86}{Orthotropic damage model with fixed crack orientations for composites - CompDamMat}{equation.1.200}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Typical loading/unloading material performance for homogenized stress and strain in the direction `${2}$'. Note that one damage parameter is common for both tension and compression.}}{87}{figure.10}}
\newlabel{comp_performance}{{10}{87}{Typical loading/unloading material performance for homogenized stress and strain in the direction `${2}$'. Note that one damage parameter is common for both tension and compression}{figure.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.8}Orthotropic elastoplastic model with isotropic damage - TrabBone3d}{87}{subsection.1.8}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.8.1}Local formulation}{87}{subsubsection.1.8.1}}
\newlabel{additiveDecomposition}{{206}{87}{Local formulation}{equation.1.206}{}}
\newlabel{constitutiveLaw}{{207}{87}{Local formulation}{equation.1.207}{}}
\newlabel{fabric}{{214}{88}{Local formulation}{equation.1.214}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.8.2}Nonlocal formulation - TrabBoneNL3d}{89}{subsubsection.1.8.2}}
\newlabel{overKappa}{{219}{89}{Nonlocal formulation - TrabBoneNL3d}{equation.1.219}{}}
\newlabel{nonLocalPlStrain}{{220}{89}{Nonlocal formulation - TrabBoneNL3d}{equation.1.220}{}}
\@writefile{lot}{\contentsline {table}{\numberline {41}{\ignorespaces CDPM2 -- summary.}}{90}{table.41}}
\newlabel{cdpm2_table}{{41}{90}{CDPM2 -- summary}{table.41}{}}
\@writefile{lot}{\contentsline {table}{\numberline {45}{\ignorespaces Orthotropic damage model with fixed crack orientations for composites -- summary.}}{91}{table.45}}
\newlabel{compdammat_table}{{45}{91}{Orthotropic damage model with fixed crack orientations for composites -- summary}{table.45}{}}
\@writefile{lot}{\contentsline {table}{\numberline {46}{\ignorespaces Anisotropic elastoplastic model with isotropic damage - summary.}}{92}{table.46}}
\newlabel{trabbone_table}{{46}{92}{Anisotropic elastoplastic model with isotropic damage - summary}{table.46}{}}
\@writefile{lot}{\contentsline {table}{\numberline {47}{\ignorespaces Nonlocal formulation of anisotropic elastoplastic model with isotropic damage -- summary.}}{93}{table.47}}
\newlabel{trabboneNl_table}{{47}{93}{Nonlocal formulation of anisotropic elastoplastic model with isotropic damage -- summary}{table.47}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.9}Material models for interfaces}{94}{subsection.1.9}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.9.1}Cohesive interface material - cohInt}{94}{subsubsection.1.9.1}}
\newlabel{eq:cohint1}{{223}{94}{Cohesive interface material - cohInt}{equation.1.223}{}}
\@writefile{lot}{\contentsline {table}{\numberline {48}{\ignorespaces Cohesive interface material -- summary.}}{94}{table.48}}
\newlabel{cohint_table}{{48}{94}{Cohesive interface material -- summary}{table.48}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.9.2}Isotropic damage model for interfaces}{95}{subsubsection.1.9.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.9.3}Simple interface material - obsolete}{95}{subsubsection.1.9.3}}
\@writefile{lot}{\contentsline {table}{\numberline {49}{\ignorespaces Simple interface material -- summary.}}{95}{table.49}}
\newlabel{simpleinterfacemat_table}{{49}{95}{Simple interface material -- summary}{table.49}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.10}Material models for lattice elements}{95}{subsection.1.10}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Working diagram of SimpleInterfaceMat.}}{96}{figure.11}}
\newlabel{SimpleInterfaceMat}{{11}{96}{Working diagram of SimpleInterfaceMat}{figure.11}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.10.1}Latticedamage2d}{96}{subsubsection.1.10.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Strength envelope of LatticeDamage2d.}}{96}{figure.12}}
\newlabel{StrengthLatticeDamage2d}{{12}{96}{Strength envelope of LatticeDamage2d}{figure.12}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Softening types of LatticeDamage2d: (a) linear softening, (b) bilinear softening, (c) exponential softening.}}{97}{figure.13}}
\newlabel{SofteningLatticeDamage2d}{{13}{97}{Softening types of LatticeDamage2d: (a) linear softening, (b) bilinear softening, (c) exponential softening}{figure.13}{}}
\@writefile{lot}{\contentsline {table}{\numberline {50}{\ignorespaces Scalar damage model for 2d lattice elements -- summary.}}{97}{table.50}}
\newlabel{latticedamage2d_table}{{50}{97}{Scalar damage model for 2d lattice elements -- summary}{table.50}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.11}Material models for steel relaxation}{97}{subsection.1.11}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.11.1}Model for relaxation of prestressing steel - SteelRelaxMat}{97}{subsubsection.1.11.1}}
\@writefile{lot}{\contentsline {table}{\numberline {51}{\ignorespaces SteelRelaxMat material model -- summary.}}{99}{table.51}}
\newlabel{steelRelax_table}{{51}{99}{SteelRelaxMat material model -- summary}{table.51}{}}
\citation{Bazant:72}
\@writefile{toc}{\contentsline {section}{\numberline {2}Material Models for Transport Problems}{100}{section.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Isotropic linear material for heat transport -- IsoHeat}{100}{subsection.2.1}}
\newlabel{IsoLET}{{2.1}{100}{Isotropic linear material for heat transport -- IsoHeat}{subsection.2.1}{}}
\newlabel{lindiffheat}{{233}{100}{Isotropic linear material for heat transport -- IsoHeat}{equation.2.233}{}}
\@writefile{lot}{\contentsline {table}{\numberline {52}{\ignorespaces Linear isotropic material for heat transport - summary.}}{100}{table.52}}
\newlabel{Isoheat_table}{{52}{100}{Linear isotropic material for heat transport - summary}{table.52}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Isotropic linear material for moisture transport -- IsoLinMoisture}{100}{subsection.2.2}}
\newlabel{IsoLinMoistureMat}{{2.2}{100}{Isotropic linear material for moisture transport -- IsoLinMoisture}{subsection.2.2}{}}
\newlabel{lindiff}{{234}{100}{Isotropic linear material for moisture transport -- IsoLinMoisture}{equation.2.234}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Isotropic material for moisture transport based on Ba\v {z}ant and Najjar -- BazantNajjarMoisture}{100}{subsection.2.3}}
\newlabel{sec:BazantNajjarMoistureMat}{{2.3}{100}{Isotropic material for moisture transport based on Ba\v {z}ant and Najjar -- BazantNajjarMoisture}{subsection.2.3}{}}
\newlabel{BNmodel:governing}{{235}{100}{Isotropic material for moisture transport based on Ba\v {z}ant and Najjar -- BazantNajjarMoisture}{equation.2.235}{}}
\@writefile{lot}{\contentsline {table}{\numberline {53}{\ignorespaces Linear isotropic material for moisture transport - summary.}}{101}{table.53}}
\newlabel{IsoLinmoistureMat_table}{{53}{101}{Linear isotropic material for moisture transport - summary}{table.53}{}}
\newlabel{BNmodel:diffusivity}{{236}{101}{Isotropic material for moisture transport based on Ba\v {z}ant and Najjar -- BazantNajjarMoisture}{equation.2.236}{}}
\@writefile{lot}{\contentsline {table}{\numberline {54}{\ignorespaces Nonlinear isotropic material for moisture transport - summary.}}{101}{table.54}}
\newlabel{BazantNajjarMoistureMat}{{54}{101}{Nonlinear isotropic material for moisture transport - summary}{table.54}{}}
\citation{Kuenzel}
\citation{Kuenzel}
\citation{Hansen}
\citation{BSB}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{102}{subsection.2.4}}
\newlabel{sec:NlIsoMoistureMat}{{2.4}{102}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{subsection.2.4}{}}
\newlabel{nlisomoisture:governing}{{237}{102}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{equation.2.237}{}}
\newlabel{nlisomoisture:ricken}{{238}{102}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{equation.2.238}{}}
\newlabel{nlisomoisture:kuenzel}{{239}{102}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{equation.2.239}{}}
\newlabel{nlisomoisture:hansen}{{240}{102}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{equation.2.240}{}}
\citation{Xi}
\citation{Xi}
\citation{Xi}
\citation{NISTIR7232}
\citation{Smilauer:09}
\newlabel{nlisomoisture:BSB}{{241}{103}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{equation.2.241}{}}
\newlabel{nlisomoisture:Xi}{{242}{103}{Nonlinear isotropic material for moisture transport -- NlIsoMoisture}{equation.2.242}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Material for cement hydration - CemhydMat}{103}{subsection.2.5}}
\newlabel{Cemhyd}{{2.5}{103}{Material for cement hydration - CemhydMat}{subsection.2.5}{}}
\@writefile{lot}{\contentsline {table}{\numberline {55}{\ignorespaces Nonlinear isotropic material for moisture transport - summary.}}{104}{table.55}}
\newlabel{NlIsoMoistureMat}{{55}{104}{Nonlinear isotropic material for moisture transport - summary}{table.55}{}}
\citation{Ruiz:01}
\@writefile{lot}{\contentsline {table}{\numberline {56}{\ignorespaces Cemhydmat - summary.}}{105}{table.56}}
\newlabel{Cemhydmat_table}{{56}{105}{Cemhydmat - summary}{table.56}{}}
\citation{Schindler:2005}
\citation{Schindler:2005}
\citation{Cervera:99}
\citation{Gawin:06a}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Material for cement hydration - HydratingConcreteMat}{107}{subsection.2.6}}
\newlabel{Affinity1}{{2.6}{107}{Material for cement hydration - HydratingConcreteMat}{subsection.2.6}{}}
\newlabel{eq:affinity1}{{246}{107}{Material for cement hydration - HydratingConcreteMat}{equation.2.246}{}}
\newlabel{eq:affinity2}{{247}{107}{Material for cement hydration - HydratingConcreteMat}{equation.2.247}{}}
\newlabel{eq:affinity3}{{248}{107}{Material for cement hydration - HydratingConcreteMat}{equation.2.247}{}}
\citation{Ruiz:01}
\@writefile{lot}{\contentsline {table}{\numberline {57}{\ignorespaces HydratingConcreteMat - summary of affinity hydration models.}}{108}{table.57}}
\newlabel{Affinity1_table}{{57}{108}{HydratingConcreteMat - summary of affinity hydration models}{table.57}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Performance of implemented hydration models: exponential model from Eq.\nobreakspace  {}(\ref  {eq:affinity1}), affinity model from Eq.\nobreakspace  {}(\ref  {eq:affinity2}), CEMHYD3D model from Subsection\nobreakspace  {}\ref  {Cemhyd}.}}{109}{figure.14}}
\newlabel{hydration_comparison}{{14}{109}{Performance of implemented hydration models: exponential model from \refeq {eq:affinity1}, affinity model from \refeq {eq:affinity2}, CEMHYD3D model from Subsection~\ref {Cemhyd}}{figure.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Coupled heat and mass transport material model - HeMotk}{109}{subsection.2.7}}
\@writefile{lot}{\contentsline {table}{\numberline {58}{\ignorespaces Coupled heat and mass transfer material model - summary.}}{110}{table.58}}
\newlabel{hemotk_table}{{58}{110}{Coupled heat and mass transfer material model - summary}{table.58}{}}
\citation{Kuenzel}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8}Coupled heat and mass transport material model - HeMoKunzel}{111}{subsection.2.8}}
\@writefile{lot}{\contentsline {table}{\numberline {59}{\ignorespaces Parameters from Kunzel's model.}}{111}{table.59}}
\newlabel{final_eq}{{251}{111}{Coupled heat and mass transport material model - HeMoKunzel}{equation.2.251}{}}
\@writefile{lot}{\contentsline {table}{\numberline {60}{\ignorespaces Coupled heat and mass transfer material model Kunzel - summary.}}{112}{table.60}}
\newlabel{hemokunzel_table}{{60}{112}{Coupled heat and mass transfer material model Kunzel - summary}{table.60}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.9}Material for unsaturated flow in lattice models -- LatticeTransMat}{113}{subsection.2.9}}
\newlabel{latticetransmat}{{2.9}{113}{Material for unsaturated flow in lattice models -- LatticeTransMat}{subsection.2.9}{}}
\newlabel{latticetransmat1}{{265}{113}{Material for unsaturated flow in lattice models -- LatticeTransMat}{equation.2.265}{}}
\newlabel{latticetransmat11}{{266}{113}{Material for unsaturated flow in lattice models -- LatticeTransMat}{equation.2.266}{}}
\newlabel{latticetransmat12}{{267}{113}{Material for unsaturated flow in lattice models -- LatticeTransMat}{equation.2.267}{}}
\newlabel{latticetransmat13}{{268}{113}{Material for unsaturated flow in lattice models -- LatticeTransMat}{equation.2.268}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.9.1}One-dimensional transport element}{113}{subsubsection.2.9.1}}
\newlabel{latticetransmat3}{{269}{113}{One-dimensional transport element}{equation.2.269}{}}
\newlabel{latticetransmat4}{{270}{114}{One-dimensional transport element}{equation.2.270}{}}
\newlabel{latticetransmat5}{{271}{114}{One-dimensional transport element}{equation.2.271}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.9.2}Constitutive laws}{114}{subsubsection.2.9.2}}
\newlabel{latticetransmat6}{{272}{114}{Constitutive laws}{equation.2.272}{}}
\newlabel{latticetransmat7}{{273}{114}{Constitutive laws}{equation.2.273}{}}
\newlabel{latticetransmat8}{{274}{114}{Constitutive laws}{equation.2.274}{}}
\newlabel{latticetransmat9}{{275}{115}{Constitutive laws}{equation.2.275}{}}
\@writefile{lot}{\contentsline {table}{\numberline {61}{\ignorespaces Material for unsaturated flow in lattice models - summary.}}{115}{table.61}}
\newlabel{Iatticetransmat_table}{{61}{115}{Material for unsaturated flow in lattice models - summary}{table.61}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Material Models for Fluid Dynamic}{116}{section.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Newtonian fluid - NewtonianFluid}{116}{subsection.3.1}}
\newlabel{NewtonianFluidMaterial}{{3.1}{116}{Newtonian fluid - NewtonianFluid}{subsection.3.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {62}{\ignorespaces Newtonian Fluid material - summary.}}{116}{table.62}}
\newlabel{NewtonianFluidMaterial_table}{{62}{116}{Newtonian Fluid material - summary}{table.62}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Bingham fluid - BinghamFluid}{116}{subsection.3.2}}
\newlabel{BinghamFluidMaterial}{{3.2}{116}{Bingham fluid - BinghamFluid}{subsection.3.2}{}}
\newlabel{eq:bigham-model}{{276}{116}{Bingham fluid - BinghamFluid}{equation.3.276}{}}
\newlabel{eq:smooth-bigham-model}{{278}{116}{Bingham fluid - BinghamFluid}{equation.3.278}{}}
\@writefile{lot}{\contentsline {table}{\numberline {63}{\ignorespaces Bingham Fluid material - summary.}}{117}{table.63}}
\newlabel{BinghamFluidMaterial_table}{{63}{117}{Bingham Fluid material - summary}{table.63}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Two-fluid material - TwoFluidMat}{117}{subsection.3.3}}
\newlabel{TwoFluidMaterial}{{3.3}{117}{Two-fluid material - TwoFluidMat}{subsection.3.3}{}}
\@writefile{lot}{\contentsline {table}{\numberline {64}{\ignorespaces Two-Fluid material - summary.}}{117}{table.64}}
\newlabel{TwoFluidMaterial_table}{{64}{117}{Two-Fluid material - summary}{table.64}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}FE\textsuperscript  {2} fluid - FE2FluidMaterial}{117}{subsection.3.4}}
\newlabel{FE2FluidMaterial}{{3.4}{117}{FE\textsuperscript {2} fluid - FE2FluidMaterial}{subsection.3.4}{}}
\@writefile{lot}{\contentsline {table}{\numberline {65}{\ignorespaces FE\textsuperscript  {2} fluid material - summary.}}{118}{table.65}}
\newlabel{FE2FluidMaterial_table}{{65}{118}{FE\textsuperscript {2} fluid material - summary}{table.65}{}}
\bibcite{Baehr:06}{1}
\bibcite{Bazant:72}{2}
\bibcite{Bazant:98}{3}
\bibcite{BSB}{4}
\bibcite{NISTIR7232}{5}
\bibcite{Cervera:99}{6}
\bibcite{Gawin:06a}{7}
\bibcite{GraJir}{8}
\bibcite{GraXenNys13}{9}
\bibcite{GraJir10}{10}
\bibcite{Gra14}{11}
\bibcite{inel}{12}
\bibcite{Hansen}{13}
\bibcite{Hoek}{14}
\bibcite{Kuenzel}{15}
\bibcite{mdm}{16}
\bibcite{Rots}{17}
\bibcite{ortiz}{18}
\bibcite{oofem}{19}
\bibcite{SimoHughes}{20}
\bibcite{Ruiz:01}{21}
\bibcite{simo}{22}
\bibcite{Schindler:2005}{23}
\bibcite{SimoPister}{24}
\bibcite{Smilauer:09}{25}
\bibcite{Vree:95}{26}
\bibcite{Xi}{27}
\bibcite{Bazant-89-I}{28}
\bibcite{Bazant-97-I}{29}
\bibcite{JirHav14a}{30}
